Reformulation of the LCC Savings in Terms of A and B Values 

DOE Distribution Transformer Negotiating Subcommittee Memo

November 28, 2011 

The LCC equation serves as the basis for both the LCC analysis and the LCC spreadsheet 

model. The LCC equation reflects both the first cost of a transformer and the present value of the 

operating costs throughout the service life of that transformer. The LCC equation is: 

LCC = FC + ∑ � OCn

(1+Drate)n

� Lifetime

n=0 .

Where:

FC = the first cost ($);

n = the index for the year of operation (n=0 is the standard year); 

Lifetime = the service life of the transformer;

OCn = the operating cost in year n, including the value of the losses and 

maintenance costs ($/yr); and 

Drate = the discount rate applied to the calculation (%). 

The first cost is the sum of three components:

FC = MFR_Price(1 + Markup) + Inst_Cost

Where:

MFR_Price = the manufacturer price as given in the engineering design table ($); 

Markup = the distributor markup (%); 

 Inst_Cost = the cost of installation ($); 

The quantity of interest is the change in LCC (ΔLCC) under a change in efficiency. A change in 

efficiency leads to both a change in first cost (ΔFC) and a change in operating cost (ΔOCn). The 

change in operating cost depends on the following parameters: 

PEgyNL = the price of energy for the no-load losses ($/kWh); 

PCapNL = the annualized price of capacity for the no-load losses ($/kW-yr); 

PEgyLL = the price of energy for the load losses ($/kWh); 

PCapLL = the annualized price of capacity for the load losses ($/kW-yr); 

EPTn = the electricity price trend factor for year n (n=0 is the standard year)

LGn = the load growth factor for year n (n=0 is the standard year) 

RMS = the annual average RMS load divided by the transformer capacity 

PRF = the peak responsibility factor

ΔNL = the change in the no-load loss rate defined by the engineering data (W)

ΔLL = the change in the load loss rate defined by the engineering data (W)

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The economic parameters, transformer lifetime, and parameters defining the loading 

characteristics are not affected by a change in efficiency. Only the first cost and the magnitude of 

the losses change when the transformer efficiency changes. 

The equation for the change in LCC can be reformulated using two parameters, ALCC and BLCC, 

that represent the total economic value of the no-load and load-losses calculated over the life of 

the transformer. This definition is conceptually the same as that used to define A and B 

parameters in the Total Ownership Cost estimates used in evaluating transformer losses. The 

practical difference is that, in the LCC, the values of ALCC and BLCC are calculated a posteriori

using the economic parameters, lifetime and loading characteristics that have been chosen from 

the statistical models used in the simulation. The equation for the change in the LCC is:

ΔLCC = ΔFC + ALCC * ΔNL + BLCC * ΔLL

The value of one watt reduction to the no-load losses is 

ALCC = (1/1000) � (8760 ∗ PEgyNL + PCapNL)

Lifetime

n=0

� EPTn

(1+Drate)n

�

The value of one watt reduction to the load losses is 

BLCC = (1/1000) � (8760 ∗ RMS2 ∗ PEgyLL + PRF ∗ PCapLL)

Lifetime

n=0

�

LGn ∗ EPTn

(1 + Drate)n�

The figures below show values of ALCC and BLCC for 1000 transformer simulations for Design 

Line 1 (liquid-immersed, 50kVa). The values of ALCC are distributed primarily between 10 and 

30 $/Watt, while the values of BLCC fall primarily between 1 and 10 $/Watt. The value of ALCC

vs. BLCC for each transformer installation is shown in the scatter plot of Figure 3. All of the 

inputs to the LCC equation are discussed in detail in Chapter 8 of the draft TSD. 

The equation for ALCC can also be written in the form:

ALCC = [(8760 ∗ PEgyNL + PCapNL)/1000] � � EPTn

(1+Drate)n

�

Lifetime

n=0

The quantity in square brackets is the value of losses over one year, and the sum is a present 

value factor that incorporates both the discounting and the electricity price trend over the life of 

the transformer. The A values currently specified by transformer purchasers tend to be much 

smaller than the ALCC values calculated here. This will be the case if the purchaser requires a 

short payback period, which is mathematically equivalent to using a large discount rate in the 

present value factor. This implies that, for the purchaser, the energy losses have no value after 

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the end of the payback period. The Department’s perspective is that the losses have value over 

the entire life of the unit, and so the value of ALCC is higher. The same argument holds for BLCC. 

Figure 1 Distribution of ALCC

Figure 2 Distribution of BLCC

Figure 3 Scatter plot of ALCC vs. BLCC

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